Internal problem ID [4938]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises.
page 46
Problem number: 27 part(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }={\mathrm e}^{x^{2}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([diff(y(x),x)=exp(x^2),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \operatorname {erfi}\left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[{y'[x]==Exp[x^2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {\pi } \text {erfi}(x) \]